1. True or False

a._____ If f(x) has a minimum at x=a, then there exists an , such that f(x) > f(a) for every x in (a- , a+ ).

b._____ The mean value theorem applies as long as the function is continuous in an interval [a, b].

c._____ If f'(x)=g'(x) then f(x)=g(x) +c, where c is a constant.

d._____ If x=c is an inflection point for f, then f(c) must be a local maximum or local minimum for f.

e._____ f(x) = ax² +bx +c, (with a 0), can have only one critical point.

f._____ Second Shape Theorem includes the converse of First Shape Theorem.

g._____ If f(x) has an extreme value at x=a then f is differentiable at x=a.

h._____ If f'(x) =0 at x=c then f has either a minimum or maximum at x=c.

i._____ If a differentiable function f has a minimum or maximum at x=c, then f'(c)=0.

j._____ If f is continuous in an open interval (a, b) then f attains maximum or minimum in (a, b).